1. Field of the Invention
The present invention relates to a geometric modeling method and an apparatus therefor capable of inputting a two- or three-dimensional shape in a computer or the like to form a shape and a scale, and performing changing (cancelling, adding, and correction) of the shape or scale.
2. Description of the Related Art
The following literatures can be referred to as materials describing relevant techniques in detail.
(1) Y. Yamaguchi, F. Kimura & P. J. W. ten Hagen, "INTERACTION MANAGEMENT IN CAD SYSTEMS WITH HISTORY MECHANISM" EUROGRAPHICS '87, 1987. PA1 (2) R. Light & D. Gossard, "Modification of geometric models through variational geometry", Computer-Aided Design, Vol. 14, No. 4, July 1982. PA1 (3) B. Aldefeld, "Variation of geometries based on a geometric-reasoning", Computer-Aided Design, Vol. 20, No. 3, April 1988. PA1 an input section for inputting a command or data for forming a two- or three-dimensional shape or changing the formed shape or scale; PA1 a processing unit for executing plot operations to form the shape or change the formed shape and scale on the basis of the command or data; and PA1 a graphic display for displaying the shape formed by the processing unit, PA1 wherein the processing unit comprises: PA1 a shape drawing operation section capable of receiving the shape and the size to execute plot operations for forming the shape or changing and forming the shape, and executing a reverse operation of the plot operation if necessary; PA1 a history memory for storing a plot method or plotted contents of each of the plot operations executed when a shape is input to form a new shape and an operation order of the plot operations as a history; PA1 a shape memory for storing a shape formed by each plot operation; and PA1 a data-base or file-searcher for, when a portion of the shape and the scale to be changed is specified, referring to the stored contents in the history memory, and searching one of the plot operations forming the specified portion to be changed, PA1 wherein plotting is executed by the plot operation searched by the data-base or file-searcher on the basis of data to be changed, thereby changing the shape and the scale.
Conventionally, geometric models such as a wireframe model, a surface model, and a solid model are used to input a two- or three-dimensional shape in a computer or the like. The wireframe model is a method of expressing a shape only by edges like a wirework. The surface model is a method of expressing a three-dimensional shape as an aggregation of its faces. The solid model is a method of expressing a three-dimensional shape including a difference between the interior and exterior of a solid into a computer. More specifically, in a known method of expressing a three-dimensional shape, faces and a relation between the faces are expressed by a relation between edges and faces and a relation between edges and points, thereby expressing how the faces are connected to form the surface of the solid (by, e.g., using an equation representing a predetermined shape or performing point-and-vector (normal vector) display), and describing that which side of each face is inside the solid.
These methods, however, aim at correctly expressing the shape of a solid in a computer. That is, a computer stores only the final shape of an input shape. Therefore, in order to correct the shape, a new shape must be formed, or the type of changing must be specified for all of shape elements such as a face, an edge, and a point to be changed upon correction. For example, even if there is only one portion to be corrected, a large number of portions must be corrected upon correction of the one portion. That is, since all the portions must be corrected in order to achieve perfect correction, a correction operation becomes very cumbersome.
In order to solve the above problem, a method has been proposed in which relations between faces or edges of a solid or equations to be satisfied are independently defined (e.g., a relation between coordinates and a distance in a space is defined as an equation, or a parallel or perpendicular relation between faces or edges is defined), and the shape is deformed on the basis of this information. In these methods, however, since additional information must be added (after shape formation) to a geometric model formed beforehand, an operation of forming the adding information becomes cumbersome. For example, in the case of a triangle as shown in FIG. 35, conditions to be satisfied by this shape are six simultaneous equations f1 to f6 shown on the left side of FIG. 35. In this case, even if one of the equations is not satisfied or another condition is added, the solution cannot be obtained. That is, a shape cannot be uniquely determined unless adding information is formed without any addition or omission.
As described above, it is difficult to cope with changing of a shape by only a geometric model. In addition, in order to realize shape changing, adding information must be independently added without any addition or omission. It is very difficult to independently define adequate adding information without any addition or omission for a corresponding partial shape such as a circle, a line segment, or a vertex of interest of a general complicated shape. In addition, since adding information must be independently formed for each partial shape, this conventional method has no sufficient versatility and therefore is not practical.